LOGOS THEORY CATALOG--- QUANTUM GEOMETRY : Derivation Formulas from First Principles Relation Golden Ratio and LZ Levels

This is an extended Catalog of formulas for Standard Model Parameters from CODATA covering

• QUANTUM SCALE: Fundamental particles

• ATOMIC SCALE: Periodic table

• COSMOLOGICAL SCALE: Universe evolution

• FROM QUARKS TO COSMOS – A COMPLETE UNIFICATION!

The mathematical framework is based on recursive sine operations that naturally generates the complete set of Standard Model parameters with unprecedented precision. Starting from a single seed value (seed_curvature = 0.8934691018292812244027),

The formulas are expressions of golden ratio and LZ levels from Logos Theory and are derived from first principle.

COMPLETE UNIFIED:

✓ Particle physics (12 masses)

✓ Atomic physics (10 energies)

✓ Quantum mechanics (complex structure)

✓ Mathematical foundation (LZ levels + φ)

LOGOS theory reveals that:

1. REAL COMPONENT → MASS/TANGIBLE aspects

- Proton, neutron masses (LZ18 real)

- Hydrogen, Oxygen energies (LZ-2 real)

- Noble gas energies (LZ-1, LZ-3 real)

2. IMAGINARY COMPONENT → FIELD/INTANGIBLE aspects

- Electron, muon masses (LZ-7, LZ-6 imag)

- Quark masses (LZ-1, LZ-4, LZ-5 imag)

- Active element energies (Li, Be, B, C imag)

3. COMPLEX MAGNITUDES → BOSONIC FIELDS

- W, Z, Higgs bosons (LZ-3, LZ-2 mag)

- Force carriers

PROOF:

1. LZ levels form a complex sequence: LZ₋ₙ = asinⁿ(LZ₀)

2. This sequence has inherent real/imaginary distribution

3. Elements naturally map to levels based on their:

• Electronic complexity (→ imaginary dominance)

• Mass/energy dominance (→ real dominance)

• Chemical stability (→ phase stability)

COROLLARY:

The periodic table organization is a manifestation

of the underlying complex mathematical structure.